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Numerade Educator



Problem 11 Medium Difficulty

Use the method of cylindrical shells to find the volume of the solid obtained by rotating the region bounded by the given curves about the x-axis.

$ y = x^{\frac{3}{2}} $ , $ y = 8 $ , $ x = 0 $


$V=192 \pi$

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Video Transcript

okay. Using the method of cylindrical shells means our radius is why our height is acts which in other words, is known as wide of the 2/3. The formula for volume is two pi times the integral from are bound 08 of the radius, which I just said is why times the height, which I said is why to the two divided by three times do you? Why, this is all in terms of wife. Let's simplify this a little bit. Before we take the integral, we end up with wide to the 5/3 do y. Now we can integrate. We're gonna be entering by using the power rule, which means we increased the exponent by 1 to 8/3. We divide by the new exponents 8/3 which in the words, means we have a coefficient of 3/8 now worth the point where we can plug, end our bounds and essentially sold. This is equivalent to two pi times three aides times to 56 which is equivalent to 192 pike. When we simplify